# Exercise-5 (CM ratio, break-even analysis, target profit analysis, margin of safety)

Following is the contribution margin income statement of a single product company:

Required:

1. Calculate break-even point in units and dollars.
2. What is the contribution margin at break-even point?
3. Compute the number of units to be sold to earn a profit of \$36,000.
4. Compute the margin of safety using original data.
5. Compute CM ratio. Compute the expected increase in monthly net operating if sales increase by \$160,000 and fixed expenses do not change.

## Solution:

### (1) Break-even point in units and dollars:

Fixed expenses/Unit contribution margin

\$300,000/\$24

12,500 units

or

(12,500 units × \$80) = \$1,000,000

### (2) Contribution margin at break-even point:

Contribution margin must be \$300,000 at break-even point because it will cover fixed costs and nothing will remain to go towards profit.

### (3) Computation of target profit:

(Fixed expenses + Target profit)/Unit contribution margin

(\$300,000 + \$36,000)/\$24

Company must sell 14,000 units of product to earn a target profit of \$36,000.

### (4) Margin of safety in dollars and percentage:

Margin of safety in dollars = Actual or budgeted sales – sales required to break-even

\$1,200,000 – \$1,000,000

\$200,000

or

Margin of safety in percentage = Margin of safety in dollars/Actual or budgeted sales

= \$200,000/\$1,200,000

=0.1667 or 16.67%

### (5) CM ratio and expected change in net operating income:

Contribution margin/Total sales

= \$360,000/\$1,200,000

= 0.30 or 30%

If the sales are increased by \$160,000 without any change in fixed expenses, the net operating income will be increased by \$48,000 as computed below:

\$160,000 × CM ratio

\$160,000 × 0.3

= \$48,000